A292919 Sum of n-th powers of odd divisors of n.

1, 1, 28, 1, 3126, 730, 823544, 1, 387440173, 9765626, 285311670612, 531442, 302875106592254, 678223072850, 437893920912786408, 1, 827240261886336764178, 150094635684419611, 1978419655660313589123980, 95367431640626, 5842587018944528395924761632, 81402749386839761113322

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Index entries for sequences related to sums of divisors

Formula

a(n) = [x^n] Sum_{k>=1} (2*k - 1)^n*x^(2*k-1)/(1 - x^(2*k-1)).

a(2^k) = 1.

Maple

f:= proc(n) local t, d;
  t:= n/2^padic:-ordp(n, 2);
  add(d^n, d = numtheory:-divisors(t));
end proc:
map(f, [$1..30]); # Robert Israel, Sep 27 2017

Mathematica

Rest[Table[SeriesCoefficient[Sum[(2 k - 1)^n x^(2 k - 1)/(1 - x^(2 k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 22}]]
f[n_] := Plus @@ (Select[Divisors[n], OddQ]^n); Array[f, 22] (* Robert G. Wilson v, Sep 26 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (d%2, d^n)); \\ Michel Marcus, Sep 08 2018

Crossrefs

Diagonal of A285425.

Cf. A000593, A023887, A082245.

Sequence in context: A051000 A132057 A363590 * A040777 A036568 A040776

Adjacent sequences: A292916 A292917 A292918 * A292920 A292921 A292922

Keyword

nonn,look

Author

Ilya Gutkovskiy, Sep 26 2017

Status

approved